The extension of the Breuil-Mézard conjecture to higher \(n\)  came later.
The case of 3-dimensional representations was considered and
partially solved by Herzig, Le and Morra [1]} and Le, Le Hung,
Levin and Morra [2]}, [3]}. The formulation stated in dimension \(n\)  in
Conjecture REF  is due to Emerton and Gee [4]}
(see also [5]}).
